Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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- Assume the following simple regression model, Y = β0 + β1X + ε ε ∼ N(0, σ^2 ) Now run the following R-code to generate values of σ^2 = sig2, β1 = beta1 and β0 = beta0. Simulate the parameters using the following codes: Code: # Simulation ## set.seed("12345") beta0 <- rnorm(1, mean = 0, sd = 1) ## The true beta0 beta1 <- runif(n = 1, min = 1, max = 3) ## The true beta1 sig2 <- rchisq(n = 1, df = 25) ## The true value of the error variance sigmaˆ2 ## Multiple simulation will require loops ## nsample <- 10 ## Sample size n.sim <- 100 ## The number of simulations sigX <- 0.2 ## The variances of X # # Simulate the predictor variable ## X <- rnorm(nsample, mean = 0, sd = sqrt(sigX)) Q1 Fix the sample size nsample = 10 . Here, the values of X are fixed. You just need to generate ε and Y . Execute 100 simulations (i.e., n.sim = 100). For each simulation, estimate the regression coefficients (β0, β1) and the error variance (σ 2 ). Calculate the mean of...arrow_forwardIn python: Modifydef clipped_hist(df, clip_threshold = 1) to plot a Gaussian distribution on top of a normalized histogram.arrow_forward1.Load the data into a python program and center it. 2.Compute the covariance matrix of the data Σ in three different ways. de. Measure the time that each function takes to compute Σ for the dataset and report it in your Solution.pdf document. Discuss the differences in terms of algorithm complexity and explain the difference in measured times. 3.Compute the eigenvectors and eigenvalues of Σ. The numpy linear algebra module referenced above has a function that can help. 4. Determine the number of principal components (PCs) r that will ensure 90% retained variance? How did you compute this? Provide a function in your code that determines r based on an arbitrary percentage α of retained variance. 5. Plot the first two components in a figure with horizontal axis (x) corresponding to the dimensions and vertical axis (y) corresponding to the magnitude of the component in this dimension. There will be 2 traces with d pointsin this figure. Include the figure in your pdf solution. Also save...arrow_forward
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